To see the effect of sample size on the maximum age 

 more clearly, we can approximate Equation (1) by 



J_ v _L + , al f + * <!* 4 t = ln * 2n + V + t 



i ; 



ln(2n + 1) 

 Hence E(t m J as —^- + t, 



(2) 



Holt (1965) presented similar findings as an 

 asymptotic result. 



The expected value of the maximum age is shown in 

 the table for three values of Z and several values of n 

 when t t equals 0. 



Increasing the sample size from 100 to 1,000 causes 

 the expected value of the maximum age to increase 

 by 437 . Increasing the sample size from 200 to 1,000 

 will cause a 277< increase. 



If the mortality rate is higher for older fish, the max- 

 imum age will increase even more slowly with increas- 

 ing sample size. For example, if the age structure is 

 governed by the Gompertz equation, the maximum 

 age in a sample tends to increase as the log of the log 

 of the sample size (Beverton 1963). 



Addendum 



Dr. W. E. Ricker (pers. commun.) has suggested that 

 a geometric mean (GM) regression would be more 

 appropriate than the ordinary predictive (arithmetic 

 mean, AM) regression for predicting values of log Z 

 since both variables are naturally variable. The re- 

 gression equation presented here can be converted 

 to a GM line by dividing the slope (b) by the square 

 root of the coefficient of determination (\r\) and pass- 

 ing the line through the point defined by the means of 

 the log transformed values of Z and t ma (Ricker 1973). 

 The means are: for mollusks, mean (In (Z)) = —0.82 1 

 and mean (In (i m J) = 2.465; for fish, -0.767 and 

 2.214; for cetaceans, -2.684 and 4.154; for all 

 groups, -1.093 and 2.585. 



GROWTH OF GERYON QUINQUEDENS 



(BRACHYURA: GERYONIDAE) JUVENILES 



IN THE LABORATORY 1 



The deep-sea red crab, Geryon quinquedens Smith, is 

 a large brachyuran of commercial interest inhabiting 

 the upper continental slope in the western Atlantic 

 Ocean from Nova Scotia to Argentina (Scelzo and 

 Valentini 1974). Studies of the biology of the species 

 have concerned distribution, abundance, and 

 bathymetric limits (Wigley et al. 1975; Haefner 

 1978); the ovarian cycle of adult females (Haefner 

 1 97 7) ; and development and behavior of larvae in the 

 laboratory (Perkins 1973; Rosowski 1979; Sulkin 

 and Van Heukelem 1980; Kelly et al. 1982). Studies 

 of the rate of growth of the species have been limited 

 to inferential analysis of size- frequency data, and it 

 appears that 13-15 molts are required for the crab to 

 grow from a carapace width of 20 mm to the max- 

 imum size of 150 mm (Haefner 1978). 



In this note we report results of a study of the effects 

 of temperature on the rate of growth of juvenile red 

 crabs in the laboratory. 



Methods 



Groups of juvenile red crabs were reared for nearly 

 1 yrat one of four temperatures: 6°, 9°, 12°, and 15°C. 

 Temperatures were chosen to approximate those of 

 bottom water at depths ranging from 200 to 2,000 m 

 in the western North Atlantic (Haefner 1978). Each 

 group at 6°, 9°, and 12°C consisted of five individuals. 

 The crabs in these groups were the progeny of one 

 female and resulted from laboratory- reared larvae. 

 The group at 15° consisted of 25 crabs. These crabs 

 were the progeny of another female whose larvae 

 were also laboratory- reared. 



During the experiment, juvenile red crabs were held 

 in darkness at ambient pressure at 35%o salinity. 

 Diet consisted of frozen brine shrimp {Artemia 

 salina), chopped mussel {Mytilus edulis), and clam 

 (Mercenaria mercenaria), and bits of muscle from 

 adult red crabs. Juveniles used in the experiment 

 were subjected to experimental conditions upon 

 molting from the megalopa stage to crab stage 1. 



Crabs in groups at 6°, 9°, and 12°C were maintained 

 individually in glass bowls (10.5 cm diameter) with a 

 shallow layer of sand and a small piece of plastic tub- 

 ing in which the crabs generally took up residence. 

 The bowls were kept in aerated aquaria containing 25 

 1 of filtered seawater. Upon molting to crab stage 4, 



'Contribution No. 1425 from the Center for Environmental Stud- 

 ies, University of Maryland, Cambridge, Md. 



FISHERY BULLETIN: VOL. 81, NO. 4, 1983. 



903 



